With the development of the electronic organ the capability of synthesizing a wide range of musical tones was made possible. Conventional electronic organs utilize a plurality of oscillators which generate sinusoidal tones at the fundamental frequency corresponding to the pitch of each note of an equal tempered scale. The outputs of the oscillators can be mixed with appropriate overtones to produce different musical sounds having complex waveforms. In at least one well known electronic organ this mixing of overtones was accomplished by means of a set of manually operated drawbars. Each drawbar selected a particular overtone and the position of the drawbar determined the relative amplitude of the selected overtone. The number of tone variations which could be selected corresponded to the product of the number of drawbars and the number of settable positions of each of the drawbars. Since the drawbars selected signals from the oscillators which generated the fundamental frequencies for the various notes in the tempered scale, the resulting overtones added by the drawbars were not true harmonics, thereby resulting in some dissonances of sound.
In my U.S. Pat. No. 3,809,786 there is described an electronic organ in which the waveform for each tone is digitally computed in real time. The amplitude of successive sample points of a complex wave shape corresponding to the selected note and tonal value are calculated by adding the amplitudes of a plurality of harmonics. The relative amplitude of each harmonic is determined by a harmonic coefficient, the coefficient values for all the harmonics being stored digitally in a harmonic coefficient memory. The coefficient values determine the relative amplitude of the sine wave harmonic components of the tone being synthesized. By selecting different coefficient values, the waveform of the tone being synthesized by the computational process described in the patent can be varied. The tonal value of the note can be selected by providing a plurality of "stops," each stop selecting a different set of coefficient values. However, this arrangement requries a separate set of coefficient values for each stop tab on the organ, which greatly limits the number of different quality tones which can be generated. Also, a large amount of memory is required to store a different set of coefficients for each tone that can be synthesized.
In my patent application Ser. No. 603,776, filed Aug. 11, 1975, entitled "Polyphonic Tone Synthesizer," now issued as U.S. Pat. No. 4,085,644 there is also described a digital device for calculating complex waveforms for synthesizing different quality tones. The musical instrument described in the copending application, in contrast to that described in the patent, does not require computation in real time. However, it does compute during a compute cycle the point-by-point variations in amplitude of a complex waveform by summing the relative amplitudes of a plurality of harmonic components of the waveform. A set of harmonic coefficients are stored in a harmonic coefficient memory in a manner similar to the harmonic coefficient memory of the above-identified patent.